There are 100 discrete intervals of integers, the ith being [Li, Ri], Li and Ri are both positive integers and smaller than or equal to 104. From each of the intervals a number is picked at random, i.e., the probability for every number to be picked in an interval is equally likely. Find out the probability, say p, that at least 40% of the picked numbers start with the digit 1. Submit the greatest integer smaller than or equal to 100p. Get the intervals here. Format is `Li Ri`.
Correct Answer: 1000 points
Incorrect Answer: 0 points
Basic application of gradient on vectors. Consider DA, DB and DC as vectors and put their sum of gradients to zero. This will be the equilibrium condition and hence, x=y=z=120o.